Lasing effects based on individual quantum dots have been investigated in optically pumped high-Q micropillar cavities. We demonstrate a lowering of the threshold pump power from a off-resonance value of 37 microW to 18 microW when an individual quantum dot exciton is on-resonance with the cavity mode. Photon correlation studies below and above the laser threshold confirm the single dot influence. At resonance we observe antibunching with g((2))(0) = 0.36 at low excitation, which increases to 1 at about 1.5 times the threshold. In the off-resonant case, g((2))(0) is about 1 below and above threshold.